Lattice Clifford fractons and their Chern-Simons-like theory

Weslei B. Fontana, Pedro R. S. Gomes, Claudio Chamon

SciPost Phys. Core 4, 012 (2021) · published 11 May 2021


We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example we build lattice fractons in odd $D$ spatial dimensions and their $(D+1)$ effective theory. The model possesses an anti-symmetric $K$ matrix resembling that of hierarchical quantum Hall states. The gauge charges are conserved in sub-dimensional manifolds which ensures the fractonic behavior. The construction extends to any lattice fracton model built from commuting projectors and with tensor products of spin-$1/2$ degrees of freedom at the sites.

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